I won't argue strongly against you, but your analogy is not entire parallel. The key pairs are not the bitcoins. The transactions are not the bitcoins. Bitcoins are an idea by consensus. What we are signing is "I send 50 bitcoins". I can say "I send you a postcard" but those are only words. The postcard might exist. The bitcoins don't. On the other hand, law seems to accept "intellectual property" as a thing with defensible and transferable ownership. I happen to disagree.

To me, it's a bit like playing tea with the stuffed animals. I can claim to pour some tea into your cup, and you can accept that I've done that, but it's all just imaginary.

EDIT: "legally binding contract" - ah yeah, OK. I hear what you are saying. But I don't think the bitcoins are the contract. The contract is "I promise to perform a series of actions that will result in a network agreeing to verify that I've performed those actions, in exchange for your pogs". If you deliver the pogs and I fail to perform the actions, then I'm acting fraudulently. I still hold that bitcoins don't exist any more than a blown kiss, whether signed or not.